Noble statesman pursuing grouse for his dinner, perhaps (4,10)
I believe the answer is:
beef wellington
'dinner perhaps' is the definition.
'noble statesman pursuing grouse' is the wordplay.
'noble statesman' becomes 'wellington' (Duke of Wellington).
'pursuing' means one lot of letters go next to another.
'grouse' becomes 'beef' ('beef' can be a synonym of 'grouse').
'wellington' put after 'beef' is 'BEEF WELLINGTON'.
'for his' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Other definitions for beef wellington that I've seen before include "dish - with 10a" , "meal" , "Meat-in-pastry dish" , "meat dish" , "Menu item" .)